On the endomorphism ring and Cohen-Macaulayness of local cohomology defined by a pair of ideals

Author(s)

Freitas, Thiago H. ^[1] ; Jorge Perez, Victor H. ^[2]

Affiliation

^[1] Univ Tecnol Fed Parana, Campus Guarapuava, BR-85053525 Guarapuava - Brazil

^[2] Univ Sao Paulo, ICMC, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: CZECHOSLOVAK MATHEMATICAL JOURNAL; v. 69, n. 2, p. 453-470, JUN 2019.
• Web of Science Citations: 0

Abstract

Let a, I, J be ideals of a Noetherian local ring (R,m,k). Let M and N be finitely generated R-modules. We give a generalized version of the Duality Theorem for Cohen-Macaulay rings using local cohomology defined by a pair of ideals. We study the behavior of the endomorphism rings of HI,Jt(M) and HI,Jt(M)), where t is the smallest integer such that the local cohomology with respect to a pair of ideals is nonzero and D(-):= Hom(R)(-, E-r(k)) is the Matlis dual functor. We show that if R is a d-dimensional complete Cohen-Macaulay ring and HI,Ji(R) = 0 for all i t, the natural homomorphism R Hom(r)(HI,Jt(K-R),HI,Jt(K-R)) is an isomorphism, where K-R denotes the canonical module of R. Also, we discuss the depth and Cohen-Macaulayness of the Matlis dual of the top local cohomology modules with respect to a pair of ideals. (AU)

• FAPESP's process: 13/20723-7 - Finiteness properties and Artinianness of formal local cohomology modules dened by a PAIs of ideals
• Grantee: Thiago Henrique de Freitas
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 12/01084-0 - Coefficients ideals for arbitrary ideals
• Grantee: Thiago Henrique de Freitas
• Support Opportunities: Scholarships in Brazil - Doctorate